Agency :
After playing out a goalless draw at the Hawthorns, Southampton were unable to break the deadlock in the first half of the second leg despite offering the greater attacking threat.
However, Russell Martin’s side required just two second-half minutes to hit the front through academy product Will Smallbone.
As West Brom searched for an equaliser, Adam Armstrong netted two goals in seven minutes to quash the visitors’ promotion hopes.
Defender Cedric Kipre scored a late consolation for the Baggies, but it did little to dampen the mood inside a jubilant St Mary’s.
Southampton will now prepare for a final clash with Leeds United at Wembley on May 26, while West Brom will have to settle for another season in the Championship.
With the majority of St Mary’s spurring them on, the Saints made a promising start to proceedings, carving out the first meaningful chance in the 16th minute.
Brooks made a darting run to meet Armstrong’s driven pass, turning the ball against the outside of the post to the relief of the West Brom contingent.
The Bournemouth loanee threatened again on the half-hour mark, with his long-range shot forcing Alex Palmer to make a save down low to his left.
Despite enjoying the majority of possession, Southampton were unable to make their dominance count before the half-time break.
However, that soon changed in the second period when Smallbone produced a thunderous strike to fire the hosts into a 49th-minute lead.
Smallbone pounced on a loose pass from Grady Diangana on the halfway line, before linking up with Brooks to create the space to power a right-foot shot past the despairing Palmer.
Southampton were then left frustrated when Brooks went down under Kipre’s clumsy challenge, only for referee Tim Robinson to wave off the vociferous penalty appeals.
Moments later, West Brom defender Darnell Furlong went agonisingly close to netting an equaliser, pouncing on a loose ball from a corner to draw a fingertip top from Alex McCarthy.